The 30-year-old Williams has never gone out before the last 16 in New York but having not played any tournaments in the lead-up because of knee tendinitis, she looked a little rusty.

But after taking the first set on the tiebreak, she slowly found her game in the second set to run out a comfortable winner.

Williams said she was not allowing herself to look any further ahead than her next opponent, Luxembourg’s Mandy Minella, a qualifier in her first grand slam event, who upset Bulgarian 32nd seed Tsvetana Pironkova 6-4 6-0.

“I’m really just going match by match,” Williams said. “I’m not thinking about dusting off any rust or where I might be.

“I thought I made a quick turnaround this summer to try to get ready (for the U.S. Open). I’m glad that I’m just in the singles as that way I have a chance to recover between rounds.